Radar, sonar, lidar, and other remote sensing techniques involve locating a target by measuring the time-of-flight of an electromagnetic pulse from an antenna to the target and back again. The farther the target is from the antenna, the longer the delay between transmission of the pulse and reception of the return signal from the target. The delay increases linearly with the range to the target, but the amplitude of the return signal varies as 1/R4, where R is the range to the target. Thus, a doubling of radar range requires a sixteen-fold increase in amplitude of the emitted pulses.
To achieve fine range resolution, the emitted pulses should have wide bandwidth. For single-frequency pulses, the bandwidth increases as the pulse width decreases, so making a single-frequency pulse shorter increases the range resolution. If the pulse amplitude remains constant, however, then the total pulse energy drops as the pulse duration decreases, causing a corresponding decrease in radar range given a constant receiver sensitivity and noise floor. Although increasing the pulse amplitude offsets the decrease in radar range due to the decrease in pulse duration, limits on peak pulse amplitude usually prevent simultaneous measurement of targets at the farther ranges with the finest possible range resolution.
Range limits imposed by peak pulse amplitude can be overcome by chirping or encoding the emitted pulses to increase their bandwidth without decreasing their duration. Because the pulse duration remains long, the total pulse energy stays high despite limits on peak pulse amplitude, allowing long range detection with fine range resolution. Spreading the pulse energy in time also causes the return signal to spread in time, which may cause the peak of the return signal to fall below detectable limits despite the fact that the return signal contains a detectable amount of energy.
Fortunately, pulse compression makes it possible to recover range information from return signals that may be obscured by noise. Pulse compression processing combines the benefits of high pulse energy and fine range resolution of long signals with the detectability of short return pulses. In pulse compression processing, a long coded or chirped return pulse is correlated against a replica of the identically coded or chirped transmitted pulse. Correlation redistributes most of the received energy into the main lobe of the correlation peak, but does not affect the distribution of noise energy. As a result, correlation has an effect similar to amplification: it increases the amplitude of the peak relative to the noise floor by an amount equal to the pulse compression factor, TΔf, where T and Δf are the duration and bandwidth, respectively, of the transmitted pulse. For more on pulse compression and radar, see M. I. Skolnik, ed., Radar Handbook (McGraw-Hill 3rd ed. 2008).
After correlation, not all of the received energy is in the main correlation peak; some energy ends up in time sidelobes on both sides of the main lobe. In some cases, time sidelobes may obscure main lobes that represent other targets. For example, if a large target and a small target are close enough to each other in the radar's field of view, they will produce returns that overlap in time. Pulse compressing the overlapping returns produces a large peak for the large target and a small peak for the small target. If the size difference between the targets is large enough, the sidelobes associated with the large target may be larger than the main lobe associated with the small target, making it difficult, if not impossible, to resolve the small target. Windowing and coding can suppress time sidelobes, but it is often difficult to eliminate time sidelobes completely, and windowing may filter out the signal from the small target as well.